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High-Resolution GNSS-Tracked Drifter for Studying SurfaceDispersion in Shallow Water
KABIR SUARA, CHARLES WANG, YANMING FENG, AND RICHARD J. BROWN
Science and Engineering Faculty, Queensland University of Technology, Brisbane, Queensland, Australia
HUBERT CHANSON
School of Civil Engineering, University of Queensland, Brisbane, Queensland, Australia
MICHAEL BORGAS
Marine and Atmospheric Research, Commonwealth Scientific and
Industrial Research Organisation, Aspendale, Victoria, Australia
(Manuscript received 30 June 2014, in final form 6 November 2014)
ABSTRACT
The use of Global Navigation Satellite System (GNSS)-tracked Lagrangian drifters allows more realistic
quantification of fluid motion and dispersion coefficients than Eulerian techniques because such drifters are
analogs of particles that are relevant to flow field characterization and pollutant dispersion. Using the fast-
growing real-time kinematic (RTK) positioning technique derived from GNSS, drifters are developed for
high-frequency (10Hz) sampling with position estimates with centimeter accuracy. The drifters are designed
with small size and less direct wind drag to follow the subsurface flow that characterizes dispersion in shallow
waters. An analysis of position error from stationary observation indicates that the drifter can efficiently
resolve motion up to 1Hz. The result of the field deployments of the drifter in conjunction with acoustic
Eulerian devices shows a higher estimate of the drifter streamwise velocities. Single particle statistical analysis
of field deployments in a shallow estuarine zone yielded estimates of dispersion coefficients comparable to
those of dye tracer studies. The drifters capture the tidal elevation during field studies in a tidal estuary.
1. Introduction
The Lagrangian technique is known to provide con-
ceptual data for observing the spatial structure of the
flow field in water bodies. These data are obtainable
either by visualization of spreading dye or the position
history of water-following parcels known as drifters. The
Lagrangian technique allows amore realistic estimate of
the scale of motion and diffusion coefficient than the
Eulerian technique because it focuses on the motion of
particles of interest. These estimates are particularly
important in marine ecological studies (Landry et al.
2009; Qiu et al. 2010) and safety measures, for example,
in the investigation of fate of contaminants (Kopasakis
et al. 2012).
In riverine and estuarine environments, a number of
theoretical and empirical dispersion models from down-
streamobservation of injection concentration using tracer
probes are available in the literature (Fischer et al. 1979;
Chanson 2004; Sundermeyer and Ledwell 2001; Situ and
Brown 2013). Tracers rapidlymix in a vertical direction as
compared to transverse direction due to the large width-
to-depth ratio of shallow waters (Swick and MacMahan
2009); thus, vertical mixing is often inferred. With tracer
technology, accurate estimation of the transverse mixing
simplifies the advection–diffusion equation to a one-
dimensional form in order to predict the longitudinal
dispersion. However, these environments are usually
unsteady with complex bathymetry and a high level of
human activities, and thus require regular monitoring.
Lagrangian drifters–floats have been widely applied
to fluid dynamics for oceans (Ohlmann et al. 2012;
Berti et al. 2011; Poje et al. 2014), lakes (Pal et al. 1998;
Stocker and Imberger 2003), and nearshore and coastal
Corresponding author address: Kabir Suara, Science and Engi-
neering Faculty, Queensland University of Technology, 2 George
St., Brisbane QLD 4000, Australia.
E-mail: [email protected]
MARCH 2015 SUARA ET AL . 579
DOI: 10.1175/JTECH-D-14-00127.1
� 2015 American Meteorological Society
regions (List et al. 1990; Spydell and Feddersen 2009;
Landry et al. 2009; Schroeder et al. 2012). Evaluation of
Surface Velocity Program (SVP) drifters applied to
ocean and large water bodies is available in Lumpkin
and Pazos (2007). The scale of motion that can be re-
solved greatly depends on the size of the parcel and
precision of position estimates. Removal of selective
availability—an intentional addition of white noise to
the global positioning system (GPS) satellite signal—
by the U.S. government on 2 May 2000 reduced the
position error estimation from 100 to 20m (D’Roza and
Bilchev 2003; Johnson et al. 2003) and hasmade it possible
forGPS drifters to be used to studying surfzone dispersion
with flow features on the order of 10m (Johnson et al.
2003; Schmidt et al. 2003; Johnson and Pattiaratchi 2004).
A drifter made from a handheld GPS unit described by
MacMahan et al. (2009) could be used to resolve flow
features in the order of 3m. Integral length in a shallow
water body (i.e., ones with depth limited to 2–3m at high
tide) is estimated by Chanson et al. (2014) to be in the
order of 1m, which requires drifters with centimeter
range position accuracy sampled at high frequency.
Improvements in the position fixing of GPS-Global
Navigation Satellite System (GNSS) hasmade accuracy at
the level of centimeters possiblewith the use of the precise
real-time kinematic (RTK) positioning algorithm and
a nearby reference station for modeling and eliminating
GPS measurement errors. An RTK data processing sys-
tem, such as the open source software Real-Time Kine-
matic Library,RTKLib (Takasu andYasuda 2009), allows
for real-time download and processing of GPS-GNSS raw
data using low-cost off-the-shelf hardware to derive pre-
cise positioning solutions (Takasu and Yasuda 2009). The
RTK–GNSS system provides a promising technique for
developing a high-resolution Lagrangian device that al-
lows for effective resolution of flow features on the order
of a few centimeters, and thus it could be used for studying
dispersion in shallow waters and estuarine systems.
The aim of this paper is to describe the performance of
evolving GNSS-tracked drifters with centimeter reso-
lution, for studying dispersion in shallow water estuar-
ies. The paper describes field observation in a typical
estuarine system using these newly developed drifters
deployed alongside a fixed acoustic Doppler velocime-
ter (ADV) and an acoustic Doppler current profiler
(ADCP). The present configuration of the drifters is
designed to follow the subsurface current that charac-
terizes horizontal dispersion in shallow water. Also de-
scribed in this paper are the results of single particle
analysis of several field deployments of these drifters.
The paper also describes the additional application in
flood height monitoring while outlining possible limita-
tions of the system.
2. Shallow water drifter design
Some primary design criteria for a shallow water
drifter include small size, large drag area ratio, and
stability during drift. Small size ensures that the drifter is
capable of operating in water depth less than 1m, min-
imizing the surface direct windage and easing the de-
ployment and retrieval during field applications. Slip is
the horizontal motion of a drifter that differs from the
motion of currents (Lumpkin and Pazos 2007). The
wind-induced current Uslip depends on both drifter drag
area ratio and wind vector in the vicinity of the
measurements. The Uslip can be described as
jUslipj5A
RUwind , (1)
where R is the ratio of drag area (product of drag co-
efficient and cross-sectional area) of the submerged
portion to that of the unsubmerged portion of the
drifter, Uwind is the downwind speed (m s21), and A 50.07 (Niiler and Paduan 1995). Therefore, the slip could
be minimized with large R, that is, minimized un-
submerged area with optimized submerged area.
The present drifter configuration is made of aluminum
machined into a hollow cylinder with an outside diameter
of 197mm and a height of 260mm (Fig. 1). Arranged
close to the base of the cylindrical aluminum capsule are
the GNSS receiver, the computing board, and direct
current (dc) batteries to power the circuit boards ar-
ranged to provide ballasting. The drifter is additionally
ballasted with steel plates to prevent overturning with
positive buoyancy, such that only 30mm from the tip of
the hull is maintained above the water surface. This en-
sures vertical separation of centers of mass and buoyancy
to reduce the heave and roll of the drifter. This configu-
ration results in an estimated wind slip Uslip of 0.03–
0.032ms21, assuming a wind of 5ms21 in the same di-
rection as the drifter using the simple model in Eq. (1).
Each drifter records and stores GNSS rawmeasurements
(pseudorange and carrier phase data) at 10Hz in the re-
ceiver for postprocessing. At this frequency, the batteries
power the drifter for up to 12h of deployment.
The spatial requirement of shallow water estuaries
includes capturing the dispersion process on the order of
the integral length scale, which is approximately half the
depth of the channel. The small spatial [O(1m)] and
short temporal [O(30 s)] scales of interest in estuaries
require centimeter accuracy with high-frequency
[O(1Hz)] data acquisition. At present, the drifter is
made to store data in a Secure Digital card while a ref-
erence station acquires data simultaneously. Upon re-
trieval, the data are postprocessed in differential mode
using RTKlib, which provides coordinates in geodetic
580 JOURNAL OF ATMOSPHER IC AND OCEAN IC TECHNOLOGY VOLUME 32
form. Further quality control is then implemented as
described in section 4.
3. Field deployment
Two field studies were conducted in Eprapah Creek,
a subtropical creek located to the southeast Queensland,
Australia (Chanson et al. 2012). The estuarine zone is
about 3.8 km long with a typical semidiurnal tidal
pattern and flows into Moreton Bay, adjacent to the
Pacific Ocean at Victoria Point (Trevethan et al. 2008).
Based on a survey carried out on 30 September 2013, the
creek has a maximum depth of 3–4m mid-estuary at
high tide with a width of about 50m at site 1A close to
Moreton Bay and 10m at site 2C (Fig. 2).
On 30 August 2013, two drifters sampling at 10Hz
were deployed two times in a cluster in an incoming tide
at the site enclosed in polyline (site 2; Fig. 2) and were
FIG. 1. (a) Photograph and (b) elevation of the GPS-tracked drifter, and (c) schematic section showing the arrangement of the internal
components and the water level.
FIG. 2. (right) Google Earth vicinity map of Eprapah Creek with (left) schematic of features shown on right, as well as the general
location within Australia of the study. At the topmiddle is the mouth of the creek close toMoreton Bay. Flood tide flows in fromMoreton
Bay through site 1A; the gray-shaded square, site 2BB, has a fairly straight portion and a semicircular meander where most deployments
were carried out. White lines in right panel show trajectories of drifters. Eprapah Creek is located at227.5678S, 153.308E. Google Earth
7.1.2.2041.
MARCH 2015 SUARA ET AL . 581
allowed to float past the semicircular meander (site 2B)
before retrieval. Also deployed was a fixed SonTek
ADV at the end of the straight part of the channel 10m
from the left bank (Fig. 2). On 30 September 2013,
several deployments weremade in an outgoing tide from
the upstream of site 2B (Fig. 2) past fixed devices for
validation. Three SonTek 16-MHz micro-ADVs were
similarly deployed at site 2B (Fig. 2). Note that this lo-
cation was the most convenient for the setup because it
has access to a boat launch and a solid bank for the data
acquisition station. The threeADVswere placed at 0.32,
0.42, and 0.55m from the bottom, respectively, and were
about 11m from the left bank of the channel. In addi-
tion, a Teledyne RD Instruments (RDI) Workhorse
ADCP was deployed. The RDI Workhorse 1200-kHz
self-logging ADCP was installed on the sediment–water
interface in an upward-looking configuration. The
ADCP was located at a transect 0.94m lower than the
bed elevation, 10.1m downstream of the ADVs, and
approximately 12.6m from the left bank, and used
a 0.05-m vertical bin size resulting into 55 bins. The
ADCP ping rate was 5.56Hz and produced averaged
data over an 854-s interval. Additional drifter de-
ployments were carried out at sites 1A and 1B (Fig. 2) to
obtain an estimate of spatial mean velocity variation
along the creek and the capability of the drifter in
measuring tidal elevation. All drifter deployments were
conducted from a small boat near the center of the
channel using a wooden frame attached to the boat to
reduce the bobbing effect and to provide estimates of
initial distances between the drifters. Concurrently for
both field trips, local tidal elevations were taken from
a fixed location close to the ADV using survey staff.
Table 1 summarizes the field conditions, the number of
drifters, the number of successful deployments, the total
drift times for the deployments, the mean velocities for
each reach, and wind slips.
4. Data processing and coordinate transformation
The GNSS receivers of the drifters were configured to
output 10-Hz raw measurements to be stored on the
computing board for postprocessing using RTKlib,
licensed under version 3 of the GNU General Public
License (GPLv3; Takasu and Yasuda 2009). The RTK
solution combined with the nearby reference station
data achieves accuracy in the order of 1 cm for fixed
solutions and about 10 cm for float solutions.
Like atmospheric flows, estuarine flows are aniso-
tropic and the correct choice of coordinates is important
(LaCasce 2008). Geographical coordinate frames are
used for drifter studies in oceans and other large bodies,
but they are not ideal for a statistical description of the
channel due to sinuosity (Swick and MacMahan 2009),
limited width, and strong streamwise velocity. From an
east, north, up (e-n-u) coordinate, the time series were
transformed to a channel-based streamwise, normal, up
(s-n-u) coordinate using the MATLAB code provided
by Legleiter and Kyriakidis (2006), with error limited to
a few centimeters. Herein for simplification, the tidal
direction is taken as positive streamwise, denoted by
subscript ‘‘s’’; the cross-shore n axis is normal to the
channel centerline and positive toward the left bank,
denoted by subscript ‘‘n’’; and the u axis is taken as
positive upward, denoted by subscript ‘‘u.’’
Quality control on the raw data includes removal of
paths associated with disturbances; proximity to obstacles–
banks of the channel; and cluster influence, based on the
event record of field studies. It was observed from the
field that spikes related to poor GPS fixes and external
disturbances resulted in acceleration greater than
1.5m s22 in the horizontal direction and 5ms22 in the
vertical direction. The time series of horizontal position
coordinates (s, n) were processed by removing errone-
ous data with acceleration greater 1.5m s22. These er-
rors occurred when the number of satellites visible to the
antenna permits the float solution (10-cm accuracy) in-
stead of the fixed solution (1-cm accuracy). The vertical
data are presented in meter Australian height datum
(mAHD) and data with acceleration greater than
5ms22 were flagged. Corrupted data in a time series
could be replaced by spline fits andmany othermethods.
Only about 2% of the data were flagged. These values
were replaced by adding displacements corresponding
to the mean track velocity to preceding positions. The
velocities and accelerations used for the quality control
TABLE 1. Summary of field deployments of drifter; wind data were taken using Vintage PRO weather station fixed at site 2.
Test Date (2013) Location Drifter tracks
Total drift
time (min)
Mean flow
speed (m s21)
Mean wind
speed (m s21)
Dominant
wind direction Uslip (m s21)
1 29 Aug Site 2 4 200 0.143 1.93 NNE 60.0121
2 30 Sep Site 2B and 2BB 4 80 0.140 1.18 NNE 60.0071
3 30 Sep Site 1A 1 36 0.240 1.42 N 60.0092
4 30 Sep Site 1B 1 40 0.190 1.34 NNE 60.0084
5 30 Sep Site 2 1 50 0.150 1.01 NNE 60.0060
582 JOURNAL OF ATMOSPHER IC AND OCEAN IC TECHNOLOGY VOLUME 32
were computed in a finite forward-differencing scheme
with N 2 1 and N 2 2 degrees of freedom, respectively.
5. Evaluation of GPS system error
Errors in position fixing using GPS are associated with
hardware, satellite clock error, and the multipath effect,
among others. These errors have been minimized in the
present drifter with the use of RTKlib software in real-
time kinematic positioning mode, which corrects the
location estimate of moving drifter with the error esti-
mated by the reference station. However, this configu-
ration still leaves some residual relative error associated
with the acquisition unit, which has to be quantified for
proper calibration of the device. To estimate the mag-
nitude of the inherent error of the drifters, it was as-
sumed that GPS position fixing is independent of drifter
motion. The actual measurement x of a continuous ob-
servation X is obtained by deducting the relative error
r [Eq. (2)]. Therefore, stationary observation is repre-
sentative of the error in motion when x 5 0. Three sta-
tionary tests at different open locations, each ranging
from 25 to 45min in length, were carried out with
a drifter coupled with all internal components and
sampling at a frequency of 10Hz,
x5X2 r (2)
Position coordinates were transformed to a local enu
coordinate and demeaned to obtain the relative errors
shown (Fig. 3a). The maximum northing and easting
position deviations were 0.025 and 0.018m with maxi-
mum standard deviations of 0.01 and 0.008m, re-
spectively. The velocities of the relative errors were
computed by central differencing (Fig. 3b) with magni-
tudes of 3.4 3 1025 6 0.0073 and 2.14 3 1025 60.0056ms21, respectively, for test 1. Table 2 shows the
error estimates from other locations. The stationary
estimates were taken from locations within a 20-km ra-
dius of the designated reference station. Thus, the sta-
tionary position estimate is representative of the relative
error and can therefore be used for quality control of the
drifter deployments made within a 20-km differential
range.
The lowmean values indicate the symmetrical nature of
relative position errors about the mean. 1The standard
deviations of the position and velocity errors are an order
of magnitude lower than those of the survey-grade Blue
Logger recording carrier phase information Ashtech
(BLASH) GPS configuration (MacMahan et al. 2009),
which has the ability to resolve flows in the order of
0.05ms21. The low magnitude of these errors demon-
strates the ability of the present drifters to obtain accurate
position and velocity measurements [O(0.09ms21)], that
is, an order of magnitude greater than the maximum ve-
locity error) for describing the dispersion process in estu-
arine environments where processes of interest occur at
small scales [O(100 s) and O(few meters)].
6. GPS error removal and drifter field performance
The removal of GPS errors existing at high frequency
from actual position data can be done by means of
low-pass filtering of the RTK positioning solution. This
requires defining the cutoff frequency, where the signal-
to-noise ratio (SNR) is less than an acceptable value. For
resolving environmental flow scales, SNR must be
greater than 10; that is, the true signal should be at least
an order of magnitude larger than the device noise
FIG. 3. Relative error obtained from stationary measurements
for test 1: (a) positions in north and east directions and (b) veloc-
ities in east (Ve) and north (Vn) directions. See Table 2 for results
for tests 2 and 3.
MARCH 2015 SUARA ET AL . 583
(Johnson et al. 2003; Johnson and Pattiaratchi 2004;
MacMahan et al. 2009). The data from the drifter test 3
at Eprapah Creek (Table 1) were used for field perfor-
mance spectra analysis. The stationary observations
were uncorrelated with the field-deployed observations;
thus, we define the spectrum of the true observations as
Sxx 5 SXX2 Srr , (3)
where Srr 5 SXXjx50 is the spectrum of stationary ob-
servation and Sxx is the spectrum of field observation.
SNRs were then obtained from Eq. (4):
SNR(f )5SXX(f )2 Srr(f )
Srr(f ). (4)
The spectra of positions and velocities were obtained by
fast Fourier transform (FFT), described in Johnson and
Pattiaratchi (2004). The length of field observation
equivalent to the stationary observation was used in
computing the SNR in order to maintain the same fre-
quency resolution. The position and velocity spectra
(Fig. 4) were computed as the average of eight overlapping
sections of 4096 points Hanning windowed at the 95%
confidence level. The position spectra of the stationary
measurement are similar in shape and trend with those
obtainedby Johnson et al. (2003), Johnson andPattiaratchi
(2004), and MacMahan et al. (2009), with magnitudes of
O(0.01m2s). The lowermagnitude is indicative of the lower
relative error when compared to previous drifters applied
in larger water bodies. The slope of the relative error
position power spectral density (PSD) between 0.001 and
0.01Hz is best fitted with a power of 1 compared with 1.3
observed by Johnson et al. (2003).
The position of the SNR (Fig. 4e) shows that the noise
level is insignificant at low frequencies—especially be-
low 1Hz, where the true signal is of an order of magni-
tude higher. The SNR went below 10 at frequencies
beyond 1.5Hz in both streamwise and cross-shore di-
rections. This suggests a cutoff frequency of fc 5 1.5Hz,
as compared to a survey-grade drifter applicable to rip
currents with a cutoff frequency of O(0.1Hz) (BLASH
configuration; MacMahan et al. 2009). The SNR of
several other portions of the field data was also tested, with
all indicating acceptable observations of frequency up to
the range of 1–2Hz. This high cutoff frequency enables
studying shallow water dispersion processes of interest
occurring at a frequency ofO(1Hz). Further analysis of the
data was done by application of low-pass filter on the
quality-controlled data using the computed cutoff fre-
quencies. This approach removes the high-frequency
content of the data where the magnitude of error is high.
The velocity SNR reveals that the drifter cross-shore
velocity data were corrupted with noise from a fre-
quency of 0.1Hz upward, while there was significant
signal level in streamwise velocities up to 1.5Hz due to
the low cross-shore velocity of the tidal channel.
The velocities of the drifters were compared with the
fixed ADVs and the ADCP sampled at transects 10.1m
apart (Fig. 5). There is difficulty in validating the drifter
measurements with Eulerian data (ADVs and ADCP)
on the field because these devices experience similar
velocity only for short times. In addition, in shallow es-
tuaries, the combined effects of tide, wind, and ba-
thymetry result in high spatial variability of velocities. In
spite of these factors, the drifter shows a similar trend in
time with that of the ADVs when the drifter was within
a 50-m streamwise radius of the ADVs. The large values
of drifter streamwise velocity are probably related to
both the wind shear on the subsurface layer of the es-
tuary and unavoidable wind drag on the unsubmerged
portion of the drifter. Figure 5b shows the postprocessed
ADCP ensembled streamwise velocity at centered time,
t 5 119 100 s, and the average of the time series (ADV
and GPS drifter) is shown in Fig. 5a. The vertical profile
of the channel streamwise velocity shows that the ve-
locity increased with relative height from the bed, sim-
ilar to steady wide open channel flow with a maximum
velocity close to the surface as indicated by the drifter
velocity and the ADCP bins next to the free surface.
This additionally validates that the drifter motion is
representative of the near-surface horizontal current
motion. The correlation of drifter velocity in the cross-
shore direction was poor, as a result of secondary flows
in the semicircular meander (sites 2B and 2BB in Fig. 2),
which the drifter could not properly resolve.
TABLE 2. Statistics of stationary tests from different locations; test 1 results are presented in Fig. 3.
Test
Distance from the
reference station
Maximum
position
error (cm)
Std dev of
position
error (cm)
Maximum velocity
error (cm s21)
Mean velocity
error (cm s21)
Std dev of velocity
error (cm)
North East North East North Vn max East Ve max North Vn East Ve North Vn std East Ve std
1 ;40m 2.50 1.80 1.00 0.83 5.58 2.90 0.0034 20.0021 0.73 0.56
2 ;50m 2.20 1.10 0.86 0.32 4.00 4.95 20.0013 0.00042 0.54 0.43
3 ;16 km 2.50 1.55 0.53 0.85 4.96 6.00 0.00033 0.00058 0.69 0.94
584 JOURNAL OF ATMOSPHER IC AND OCEAN IC TECHNOLOGY VOLUME 32
7. Diffusion estimate
Statistical analysis of Lagrangian data is mostly con-
cerned with either single particles or the relative motion
of groups of particles (Berti et al. 2011). Single particle
analysis of tracked drifters has been used to identify the
underlining dynamics in the atmospheres and oceans
(LaCasce 2008). The basic application of single particle
analysis to an estuarine environment is the estimate of
the absolute diffusivity.
The horizontal position coordinates of the quality-
control data (Table 1; test 1) were low-pass filtered with
a cutoff frequency of fc5 1.5Hz. The decorrelation time
scale for the individual drifters was estimated from the
autocorrelation function of residual velocities obtained
upon removal of the averaged velocity and was found to
FIG. 4. Spectral analyses of a 34-min signal. (a) Relative position error from stationary record, converted to local
east and north coordinates. (b) Velocity computed from stationary records. (c) Field observation in local
streamwise and cross-shore coordinates. (d) Velocity for field deployment. All power spectral densities are aver-
aged estimates of eight 50% overlapping sections of 4096 points with each section windowed with a Hanning
window. (e) SNR for the displacement measurement and (f) SNR for the velocity measurement using the drifter.
MARCH 2015 SUARA ET AL . 585
be 50 and 15 s in the streamwise and cross-shore di-
rections, respectively. The diffusivity estimates pro-
ceeded with the basic assumptions of homogeneity and
stationarity of the residual flow field. Therefore, the
position time series were separated into short in-
dependent realizations with time intervals greater than
the decorrelation time to obtain the displacement time
series. Figure 6 shows 20 realizations of the displace-
ment time series, each of 10min long. The normalized
density of the displacement time series gives the prob-
ability distribution function (PDF). The variances (ab-
solute dispersions) were estimated from the PDF,
thence the absolute diffusivity, which is the rate of ab-
solute dispersion with time. Herein, the absolute dis-
persion coefficient is obtained as the slope of absolute
dispersion with respect to time by linear regression for
times t. 100 s, times greater than the decorrelation time
scale (Taylor 1921; Berti et al. 2011). The dispersion co-
efficient varied with the length of short realizations. The
maximum absolute streamwise dispersion coefficient
Kss 5 0.57m2 s21 was obtained with 16-min realization
length, while that of the cross-shore direction Knn 50.053m2 s21 was obtainedwith 5.6-min realization length.
Many prior estimates of estuarine–coastal water dif-
fusivity used observation from tracer dyes to obtain
dispersion coefficients. The minimum lateral dispersion
coefficient for 19 sites in the United Kingdom ranged
from 0.003 to 0.42m2 s21 (Riddle and Lewis 2000). Un-
like the present observation, where the ensemble aver-
age of the group of realizations is used in the estimate,
the values reported by Riddle and Lewis (2000) were
based on individual realizations. Despite the differences
in approach, the lateral dispersion coefficient, Knn 50.028m2 s21, in the present work is within range. The
values Kss 5 0.57m2 s21 and Knn 5 0.053m2 s21 are also
in range with estimates using the GPS drifter in North
Fork Skagit River—a similar meandering river in the
United States—where Kss 5 0.39m2 s21 and Knn 50.09m2 s21 were obtained. Table 3 shows the estimates
of dispersion coefficient in similar shallow water bodies.
Using the displacement time series shown in Fig. 6,
higher-order moments of the displacement PDF were
calculated. The skewness has nonzero values ranging from
20.8 to 0.4 in the cross-shore direction and between 0.4
and 0.8 in the streamwise direction. This is a result of in-
homogeneity of the dataset. The values of kurtosis in the
cross-shore direction are not significantly different from 3,
the expected value for normal distribution. In addition, the
cross-shore diffusion coefficient decreased with an in-
crease in the length of realizations beyond 5.6min. These
results suggest that the cross-shore spreading is sub-
diffusive at times greater than 5.6min. On the other hand,
the kurtosis values aremostly around 2.5 in the streamwise
direction and the diffusion coefficient increased with lon-
ger segments. These suggest that the streamwise dis-
placement contains strong advection and is superdiffusive.
8. Limitations and benefits of present GPS drifter
The use of a GPS-tracked drifter in studying the dy-
namics of shallow coastal water has many advantages
FIG. 5. (a) Eprapah Creek streamwise velocity profiles (Table 1; test 2) averaged over 30 s measured by the GPS drifter. (b) Vertical
profile of average streamwise velocity as a function of height z from the bed normalized by water depth h, where the asterisks indicate
values measured by the upward-looking ADCP placed on the stream bed, 10.1m downstream of the ADV transect. The GPS drifter was
within 50m streamwise of the ADV transect.
586 JOURNAL OF ATMOSPHER IC AND OCEAN IC TECHNOLOGY VOLUME 32
over existing dye tracer technology and acoustic Euler-
ian devices, including flexibility of usage, lower cost, and
higher spatial coverage. Despite these advantages, there
are methodical and practical limitations with this ap-
plication. These limitations include but are not limited
to the inevitable wind-induced pseudo-Lagrangian be-
havior, the inability of the drifter to resolve small-scale
motion, and the irresponsiveness of the drifter to the
true vertical motion. Although the present drifter is
designed such that only 30-mm height is exposed to di-
rect wind drag, the wind effect could inconsistently in-
fluence the path of the drifter. This false movement,
however, could not be totally eliminated and thus re-
quires consideration when interpreting results from
drifter studies, particularly in low current speed
applications. The present drifter configuration has
a drag area ratio of 8.5–13 and a velocity difference at-
tributed to wind of less than 1% of wind speed using
a simple empirical model (Niiler and Paduan 1995). The
drifter configuration is designed for shallow water bod-
ies with relatively small wave motion. Application of the
drifter to deeper water bodies requires a slight modifi-
cation that includes the addition of a window shade or
parachute drogues to increase the drag area ratio and to
reduce the effects of wave rectification.
In environmental flows, the scale of motion ranges
from the energy containing large eddies (mean flow) to
the smallest eddies (turbulent fluctuations). A drifter
functions as a filter that only captures motion on a scale
greater than its radius. Thus, the drifter size limits the
FIG. 6. Displacement time series for segmented drifter trajectories with average displacement
in bold: (a) streamwise component and (b) cross-shore component.
MARCH 2015 SUARA ET AL . 587
range of eddies captured. Similarly, the high noise level
at the high frequency obtained from evaluation imposes
limits (cutoff frequencies) on the frequency content that
the drifter could reliably acquire. A relevant dataset is
the eddy viscosity data reported by Trevethan et al. (2006)
with eddy viscosities between 0.00001 and 0.001m2 s21.
The eddy viscosity is two orders of magnitude lower than
the dispersion coefficients obtained with the GNSS-
tracked drifters, suggesting large a Péclet number indrifter motion, that is, a large dispersion-to-diffusion ratio.Likewise, limitations in vertical motion as a result of con-stant density of the drifter are a clear disadvantage ofdrifter dispersion when compared with tracer dye disper-sion, which mixes both vertically and horizontally. Thus,
TABLE 3. Diffusivity estimates for shallow riverine and estuarine environment based on dye tracer technology and evolving GPS-tracked
drifter technology.
Location Year Method
Tidal
current
(m s21)
Depth
(m)
Cross-shore
Knn (m2 s21)
Streamwise
Kss (m2 s21) Source
Irvin Bay, United Kingdom* 1972 Dye tracer 0.06 6 0.05 — (Riddle and Lewis 2000)
Plym Estuary, United
Kingdom*
1973 Dye tracer 0.15 4 0.01 — (Riddle and Lewis 2000)
Tee Estuary, United Kingdom* 1978 Dye tracer 0.15 3 0.05 — (Riddle and Lewis 2000)
Poole Estuary, United
Kingdom* (flood tide)
1979 Dye tracer 0.75 1.8 0.014 — (Riddle and Lewis 2000)
Yantze–China 1999 Dye tracer 0.5 5 0.88 — (Riddle and Lewis 2000)
North Fork Skagit, United
States
2008 GPS drifter 0.55 — 0.09 0.39 (Swick and MacMahan 2009)
Upper estuary, Eprapah Creek,
Australia (flood tide)
2013 GPS drifter 0.14 3 0.053 0.57 Present study
* Values are minimum estimates for the area.
FIG. 7. (top) Eprapah Creek tidal elevation between 29 Sep and 1 Oct 2013 obtained from
survey staff close to the ADV at site 2BB, corrected to mAHD based on height of the Victoria
Point station above the lowest astronomic tides. (bottom) Rectangular-boxed area in
(a) showing drifter-measured elevation (1 signs), despiked, and low-passed filtered at 0.5Hz. Each
of the three segments denotes a separate run. The solid line segments represents the elevation
from a fixed local station. All times synchronized in seconds and taken from 0000 Australian
standard time 29 Sep 2013.
588 JOURNAL OF ATMOSPHER IC AND OCEAN IC TECHNOLOGY VOLUME 32
surface-only observation gives a biased approximation ofthe estuarine mixing as a two-dimensional phenomenon.Though vertical displacement of drifters does not
amount to dispersion, drifters move with the rise and fall
of the current. The high resolution of the present drifter
makes it sensitive to displacement as low as 1 cm. The
upward displacements were obtained from the trans-
formation fromGPS height tomAHDusingAUSGeo09
as detailed in Brown (2010) after which a low-pass filter
with a cutoff frequency of 0.5Hz was applied to elimi-
nate noise at high frequency. Figure 7 shows the plot of
the tidal elevation from the GPS validated with the local
tidal elevation in AHD against the synchronized time.
The drifter data compares well with the local tidal ele-
vation. In addition, a low-frequency wave causing the
rise and fall in the tidal height is observed, which could
be analyzed to establish its contribution to the overall
mixing in the water body. This makes the present drifter
modifiable for flood height monitoring, where drifters
could be free floating or moored while providing real-
time, near-continuous height and flow dynamics
information.
9. Conclusions
The advancements in GNSS–RTK coupled technol-
ogy have paved the way for centimeter-resolution
tracking, thus allowing the study of finescale flow dy-
namics at higher temporal resolution compared to ex-
isting drifters. Field studies were conducted using the
newly developed drifters in a shallow estuary, Eprapah
Creek, at Victoria Point, Queensland, Australia. Data
obtained from both the stationary and field studies
provided an estimate of the SNR where the drifter
showed efficient performance up to a frequency of
1.5Hz for displacement measurement. Single particle
analysis was used to obtain the absolute dispersion from
several realizations, hence diffusivities (Kss 5 0.57m2 s21
and Knn 5 0.053m2 s21), are obtained that agree well
with the estimate for similar water bodies. Further field
deployments of the developed drifters are being carried
out at Eprapah Creek to estimate the spatial and tem-
poral variability of dispersion coefficients along the tidal
channel. The vertical position coordinates of the field
deployment reveal that high-resolution GPS-tracked
drifters are applicable to flood height monitoring. An
extensive study using both dye tracer and drifters under
the same condition is required to quantify the compro-
mise of surface-only dispersion estimates in shallow
water estuaries.
Acknowledgments. The authors wish to thank all the
people who participated in the field study; those who
assisted with the preparation and data analysis; and the
QueenslandDepartment of Natural Resources andMines,
Australia, for providing access to the SunPOZnetwork for
reference station data used for RTK postprocessing.
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